The German name Österreich can be translated into English as the "eastern realm",
which is derived from the Old German Ostarrîchi. The name was
Latinized as "Austria", although it has no etymological connection
with the name of Australia (which derives from Latin Australis meaning
The South). Reich can also mean "empire," and this connotation is the
one that is understood in the context of the Austrian/Austro-Hungarian Empire,
Holy Roman Empire, although not in the context of the modern Republic of Österreich.

The term probably originates in a vernacular translation of the Medieval Latin name for the
region: Marchia orientalis, which translates as "eastern marches" or "eastern borderland",
as it was situated at the eastern edge of the Holy Roman Empire, that was also mirrored
in the name Ostmark, for a short period applied after Anschluss to
Germany.

Courtesy:Metapedia

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